When the players train in the off season do their stats increase randomly or is it effected by anything you can control?
Very random. Most of the time, I have a linemen that'll go from 68 to 76 or something like that, even if I had a player that had an All-American year and isn't that good ratings-wise. That said, I think you can save right before the training and if you don't like the results, reload it and sim it again.
It's random. The only thing you can control is your team and their "Pro Potential & Athletic Facilities". I.E. recruits at USC are going to progress far better than they would at ARMY.